Gauge anomalies on S2 and group extensions

Abstract

A geometric connection is established between the group cocycle used by Mickelsson [Topological and Geometrical Methods in Field Theory (World Scientific, Singapore, 1986), pp. 117–131] to realize the Kac–Moody extension of the group of loops in SU(n) as the quotient of a topologically trivial extension of maps from the disk into SU(n) and the gauge anomaly for Quillen’s determinant bundle over the Cauchy–Riemann operators on the spin bundle over S2.